A Molecular Mechanism for Azeotrope Formation in Ethanol/benzene Binary Mixtures Through Gibbs Ensemble **Monte** **Carlo** Simulation

**Monte**

**Carlo**(GEMC) simulation is performed to predict the VLE phase diagram, including an azeotrope point. Expand abstract.

**Monte**

**Carlo**(GEMC) simulation is performed to predict the VLE phase diagram, including an azeotrope point. The results accurately agree with experimental measurements. We argue that the molecular mechanism of azeotrope formation cannot be fully understood by studying the mixture liquid-state stability at the azeotrope point alone. Rather, azeotrope occurrence is only a reflection of the changing relative volatility between the two components over a much wider composition range. A thermodynamic criterion is thus proposed based on the comparison of partial excess Gibbs energy between the components. In the ethanol/benzene system, molecular energetics shows that with increasing ethanol mole fraction, its volatility initially decreases but later plateaus, while benzene volatility is initially nearly constant and only starts to decrease when its mole fraction is low. Analysis of the mixture liquid structure, including a detailed investigation of ethanol hydrogen-bonding configurations at different composition levels, reveals the underlying molecular mechanism for the changing volatilities responsible for the azeotrope.

10/10 relevant

chemRxiv

A **Monte** **Carlo**-Based Outlier Diagnosis Method for Sensitivity Analysis

**Monte**

**Carlo**evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, overidentifications and statistical overlap associated with IDS in the presence of a single outlier. Expand abstract.

**Monte**

**Carlo**. This paper provides the first results about

**Monte**

**Carlo**-based critical value inserted to different scenarios of correlation between the outlier statistics. From the

**Monte**

**Carlo**evaluation, we compute the probabilities of correct identification, missed detection, wrong exclusion, overidentifications and statistical overlap associated with IDS in the presence of a single outlier. Based on such probability levels we obtain the Minimal Detectable Bias (MDB) and Minimal Identifiable Bias (MIB) for the case where IDS is in play. MDB and MIB are sensitivity indicators for outlier detection and identification, respectively. The results show that there are circumstances that the larger the Type I decision error (smaller critical value), the higher the rates of outlier detection, but the lower the rates of outlier identification. For that case, the larger the Type I Error, the larger the ratio between MIB and MDB. We also highlight that an outlier becomes identifiable when the contribution of the measures to the wrong exclusion rate decline simultaneously. In that case, we verify that the effect of the correlation between the outlier statistics on the wrong exclusion rates becomes insignificant from a certain outlier magnitude, which increases the probability of identification.

10/10 relevant

Preprints.org

A **Monte** **Carlo** EM Algorithm for the Parameter Estimation of Aggregated
Hawkes Processes

**Monte**

**Carlo**Expectation-Maximization (MC-EM) algorithm. Expand abstract.

**Monte**

**Carlo**Expectation-Maximization (MC-EM) algorithm. Through a detailed simulation study, we demonstrate that existing methods are capable of producing severely biased and highly variable parameter estimates and that our novel MC-EM method significantly outperforms them in all studied circumstances. These results highlight the importance of correct handling of aggregated data.

10/10 relevant

arXiv

Markov Chain **Monte** **Carlo** Methods, a survey with some frequent
misunderstandings

7/10 relevant

arXiv

Unit Testing for MCMC and other **Monte** **Carlo** Methods

**Monte**

**Carlo**methods, this allows testing, for example, if a sampler has a specified distribution or if a sampler produces samples with the desired mean. Expand abstract.

**Monte**

**Carlo**methods as well as of general

**Monte**

**Carlo**methods. Based on statistical hypothesis tests, these approaches can be used in a unit testing framework to, for example, check if individual steps in a Gibbs sampler or a reversible jump MCMC have the desired invariant distribution. Two exact tests for assessing whether a given Markov chain has a specified invariant distribution are discussed. These and other tests of

**Monte**

**Carlo**methods can be embedded into a sequential method that allows low expected effort if the simulation shows the desired behavior and high power if it does not. Moreover, the false rejection probability can be kept arbitrarily low. For general

**Monte**

**Carlo**methods, this allows testing, for example, if a sampler has a specified distribution or if a sampler produces samples with the desired mean. The methods have been implemented in the R-package MCUnit.

10/10 relevant

arXiv

A piecewise deterministic **Monte** **Carlo** method for diffusion bridges

**Monte**

**Carlo**methods, our approach works well in case of strong nonlinearity in the drift and multimodal distributions of sample paths. Expand abstract.

**Monte**

**Carlo**methods, our approach works well in case of strong nonlinearity in the drift and multimodal distributions of sample paths.

10/10 relevant

arXiv

Newtonian **Monte** **Carlo**: single-site MCMC meets second-order gradient
methods

**Monte**

**Carlo**(NMC), is a method to improve MCMC convergence by analyzing the first and second order gradients of the target density to determine a suitable proposal density at each point. Expand abstract.

**Monte**

**Carlo**(MCMC) is a variant of MCMC in which a single coordinate in the state space is modified in each step. Structured relational models are a good candidate for this style of inference. In the single-site context, second order methods become feasible because the typical cubic costs associated with these methods is now restricted to the dimension of each coordinate. Our work, which we call Newtonian

**Monte**

**Carlo**(NMC), is a method to improve MCMC convergence by analyzing the first and second order gradients of the target density to determine a suitable proposal density at each point. Existing first order gradient-based methods suffer from the problem of determining an appropriate step size. Too small a step size and it will take a large number of steps to converge, while a very large step size will cause it to overshoot the high density region. NMC is similar to the Newton-Raphson update in optimization where the second order gradient is used to automatically scale the step size in each dimension. However, our objective is to find a parameterized proposal density rather than the maxima. As a further improvement on existing first and second order methods, we show that random variables with constrained supports don't need to be transformed before taking a gradient step. We demonstrate the efficiency of NMC on a number of different domains. For statistical models where the prior is conjugate to the likelihood, our method recovers the posterior quite trivially in one step. However, we also show results on fairly large non-conjugate models, where NMC performs better than adaptive first order methods such as NUTS or other inexact scalable inference methods such as Stochastic Variational Inference or bootstrapping.

10/10 relevant

arXiv

Quantum **Monte** **Carlo** simulation of intervortex potential in
superconductors

**Monte**

**Carlo**simulation. Expand abstract.

**Monte**

**Carlo**simulation. The vortex-vortex potential is attractive (type-I), repulsive (type-II), and flat (critical) depending on a coupling constant. The vortex-antivortex potential also depends on the coupling constant at long range but is always attractive at short range.

10/10 relevant

arXiv

Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum **Monte**
**Carlo**: Application to the Spin Gaps of the C$_{36}$ Fullerene and an Iron
Porphyrin Model Complex

**Monte**

**Carlo**(ph-AFQMC) can be reliably performed with a single-determinant trial wavefunction with essential symmetry breaking. We first utilized essential time-reversal symmetry breaking with ph-AFQMC to compute the triplet-singlet energy gap in the TS12 set. We found statistically better performance of ph-AFQMC with complex-restricted orbitals than with spin-unrestricted orbitals. We then showed the utilization of essential spin symmetry breaking when computing the single-triplet gap of a known biradicaloid, C$_{36}$. ph-AFQMC with spin-unrestricted Hartree-Fock (ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no biradicaloid character. With approximate Br{\"u}ckner orbitals obtained from regularized orbital-optimized second-order M{\o}ller-Plesset perturbation theory ($\kappa$-OOMP2), ph-AFQMC quantitatively captures strong biradicaloid character of C$_{36}$. Lastly, we applied ph-AFQMC to the computation of the quintet-triplet gap in a model iron porphyrin complex where brute-force methods with a small active space fail to capture the triplet ground state. We show unambiguously that neither triplet nor quintet is strongly correlated using UHF, $\kappa$-OOMP2, and coupled-cluster with singles and doubles (CCSD) performed on UHF and $\kappa$-OOMP2 orbitals. There is no essential symmetry breaking in this problem. By virtue of this, we were able to perform UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground state for this model geometry. The largest ph-AFQMC in this work correlated 186 electrons in 956 orbitals. Our work highlights the utility, scalability, and accuracy of ph-AFQMC with a single determinant trial wavefunction with essential symmetry breaking for systems mainly dominated by dynamical correlation with little static correlation.

10/10 relevant

arXiv

A Bayesian **Monte**-**Carlo** Uncertainty Model for Assessment of Shear Stress Entropy

**Monte**-

**Carlo**(BMC) uncertainty method is simplified considering a 95% Confidence Bound (CB). Expand abstract.

**Monte**-

**Carlo**(BMC) uncertainty method is simplified considering a 95% Confidence Bound (CB). We developed a new statistic index called as FREEopt-based OCB (FOCB) using the statistical indices Forecasting Range of Error Estimation (FREE) and the percentage of observed data in the CB (Nin), which integrates their combined effect. The Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, had the highest certainty in the calculation of shear stress values in circular channels followed by traditional uniform flow shear stress and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy with much higher values of FOCB equal to 57.726 has less certainty in the estimation of shear stress than other models. Using the presented results in this study, the amount of confidence in entropy methods in the calculation of shear stress to design and implement different types of open channels and their stability is determined.

10/10 relevant

Preprints.org